The value of context

First of all, if you have yet to read Joe Posnanski’s thoughts on Wins Above Replacement (WAR), do yourself a favor and give it a few minutes of your time. Posnanski, with his authentic writing style, wide-ranging appeal and rational thought process, just might be the perfect writer to bridge the gap between old-school baseball fans and Excel-operating baseball nerds.

Posnanski does an excellent job of discussing WAR as a concept, mostly leaving the advanced mathematics at the door. But he doesn’t mention a key point, one that I think leads to much of the arguing about the metric. WAR is a context-neutral statistic. While this is also true of many accepted stats, such as batting average, on-base percentage and slugging percentage, it seems to hurt the credibility of WAR to a greater extent. WAR is often framed as an all-encompassing stat, one that attempts to measure a player’s overall value to his team. Describing a stat as comprehensive, despite its disregard toward a player’s high-leverage performance, immediately damages its trustworthiness in many fans’ eyes. As an example, maybe you have heard this debate, or a similar one, at some point during the 2010 season.

Person A: “Lastings Milledge needs to go. His bat is awful for a corner outfielder and he’s a mess in the field and on the bases.”

Person B: “No way, Milledge has been one of the more valuable hitters on the team. He’s been huge with runners in scoring position, delivering numerous key hits.”

Which person is correct? Well, they both are. They are just looking at the situation from two different angles. Milledge has certainly been more valuable this season than his WAR, slugging percentage and other context-neutral stats would indicate. Generally speaking, his hit distribution has leaned heavily toward the more important situations, which certainly contain additional value. Unfortunately, it is not a sustainable skill. Person B is correct if we want to know how valuable Milledge was in 2010. Person A is correct if we are assessing Milledge’s true talent level based on his 2010 performance.

As Pirates fans in the year 2010, we should generally be looking at stats that are context-neutral. Determining Milledge’s value to the current team is essentially irrelevant, because there is little difference between winning 52 games or 61 games or 68 games. Gauging what Milledge’s 2010 performance means for his future performance (in other words, his value at a time when the Pirates may actually be competitive) is a much more pertinent issue and, unfortunately, his production in crucial situations possesses almost zero predictive value.

Having said all that, let’s take a look at the Pirates’ most valuable hitters in 2010. First, we will look at it from a context-neutral (and more predictive) point of view. To do that, we will use the “Offense” component of WAR, which is based on Weighted On-Base Average (wOBA). Essentially, a player is credited with a certain run value for every positive outcome (home run, stolen base, walk, etc.) and compared to league average (0 runs). Here are the top five Pirates thus far in 2010.

Next, let’s look at the team’s most valuable hitters without removing context. Win Probability Added (WPA) is an excellent metric for determining a player’s true effect on the game situation. For those unfamiliar with WPA, every point in a baseball game is broken down based on four categories: inning, score, outs and baserunners. At any instant, using decades of precedent, we can measure a team’s probability of winning a game based on the situation. That probability is called Win Expectancy (WE). For example, if the home team is batting with zero outs and the bases loaded in the seventh inning of a tie game, that team has an 82.7% chance of winning. With two outs and the bases empty in the ninth inning, trailing by one run, that team has a 4.2% chance of winning. By measuring the team’s WE both before and after an individual player’s plate appearance, we can calculate the degree to which that player either added to or subtracted from his team’s chances of winning. This allows us to accurately quantify the difference between, “Player X is more valuable than his numbers because he regularly makes productive outs” and, “Player Y is overvalued by his stats because he racks up solo home runs late in blowout games.” As you can see, the two lists essentially match, with Milledge sneaking into the WPA top five.